Final answer:
To find the number of students who play on exactly two teams, we can use sets and Venn diagrams. By representing the teams as sets A, B, and C, and using the given ratio, we can solve for the number of students in each set and the intersection of sets. And by adding the sizes of the overlapping regions, we can find the number of students who play on exactly two teams.
Step-by-step explanation:
To find the number of students who play on exactly two teams, we need to use the concept of sets and Venn diagrams. Let's label the three teams as A (basketball), B (soccer), and C (mathletics). We are given that the ratio of the sizes of the teams is 4:3:2.
We know that 8 students play all three sports, so we can place them in the intersection of all three sets (A∩B∩C).
Since half of the students play basketball, we can represent this as A/2.
Using the given ratio, we can express the sizes of the sets as 4x, 3x, and 2x respectively, where x is a common factor. Now we can fill in the Venn diagram and solve for x, which represents the total number of students at the school.
Finally, to find the number of students who play on exactly two teams, we can add the sizes of the overlapping regions (A∩B, B∩C, and C∩A).